Two-parameter families of uniquely extendable Diophantine triples

2016/11/26 by Mihai Cipu, Cipu, Mihai, Yasutsugu Fujita +3
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1611.08646

Abstract

Let A,K be positive integers and u=-2,-1,1 or 2. The main contribution of the paper is a proof that each of the D(u²)-triples K,A²K+2uA,(A+1)²K+2u(A+1) has unique extension to a D(u²)-quadruple.

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